By revisiting the famous problem — which was controversially solved in the 1970s with the help of computers — mathematicians have gained important new insights into the nature of graphs. The four-color theorem is simple to state: Given a contiguous map, is it possible to color each region with one of four colors such that no neighboring regions share a color? Vico Santos for Quanta Magazine Introduction Some math problems continue to haunt researchers long after they’ve been solved. A proof emer...